The structure of finitely generated shift-invariant subspaces on locally compact abelian groups

DOI10.1007/s00009-020-01677-2zbMath1466.43003OpenAlexW3118607470MaRDI QIDQ2222879

Soheila Jokar, Seyyed Mohammad Tabatabaie, Rajab Ali Kamyabi-Gol, Kazaros Kazarian

Publication date: 27 January 2021

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-020-01677-2

zbMATH Keywords

Fourier transformlocally compact groupsshift-invariant subspacessummation basis

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items

B-spline quarklets and biorthogonal multiwavelets, Rationally sampled Gabor frames on the half real line

Cites Work

• Unnamed Item
• Unnamed Item
• The structure of translation-invariant spaces on locally compact abelian groups
• Harmonic analysis of probability measures on hypergroups
• Spaces with an abstract convolution of measures
• The structure of finitely generated shift-invariant spaces in \(L_ 2(\mathbb{R}^ d)\)
• The structure of shift-invariant subspaces of \(L^2(\mathbb{R}^n)\)
• A characterization of admissible vectors related to representations on hypergroups
• Shift-invariant spaces on LCA groups
• Subspaces of \(L^2(G)\) invariant under translation by an abelian subgroup
• The structure of shift invariant spaces on a locally compact abelian group
• Reproducing formulas for generalized translation invariant systems on locally compact abelian groups
• Frames and Stable Bases for Shift-Invariant Subspaces of L₂(ℝ^d)
• An introduction to frames and Riesz bases